Probability Lesson Plan



Probability Lesson Plan

Name: Paul Wilson

Grade Level: 3rd Grade

Content Area: Data Analysis and Probability

Subject Matter with the Content Area: Probability

State Adopted Textbook: Houghton Mifflin California Math

Van de Walle chapter/page reference: Chapter 23/Pgs. (475-490)

2. Standards-based Learning Objective:

The students will decide if an event is certain, likely, unlikely, or impossible, as measured by completing pp.498-500 (Lesson 2) of Houghton Mifflin Mathematics with at least 80% accuracy.

3. California Mathematics Content Standard:

a. SDAP 1.1: Students understand and identify whether common events are certain, likely, unlikely, or improbable.

b. This lesson is the second lesson in the twenty third chapter of the textbook. The lesson sequence in the chapter is the following: (1) Record Outcomes; (2) Probability; (3) Make Predictions; (4) Make Predictions Pt. 2; and (5) Field Trip. The first lesson in this chapter is a hands-on lesson on how to record and display results of probability experiments. In the subsequent lesson, students conduct probability experiments and predict outcomes. The Preview-Review activity and the game “Grab Bag” will be utilized to set up the lesson as well as the chapter.

c. This lesson is in one of the later chapters of this book and students may be looking forward to summer vacation. Due to this, it is anticipated that students may wander and be less focused on tasks and instructions given. It is also anticipated that students may confuse probability words. Due to a variety of different types of students in the class such as EL and Advanced Learners, it is anticipated that students may work in pairs or even groups during the entire lesson. It is anticipated that repetition may be necessary for EL students. It is also anticipated that students will work together to solve problems and answer questions. Furthermore, it is anticipated that students will enjoy the preview-review and the “Grab Bag” game.

4. Materials

Paper Squares: (5 red, 5 blue) per group (10)

Ziploc bags for squares: per group (10)

White Board

Dry Erase Markers (Red, Blue, Orange)

Houghton Mifflin Mathematics Chapter 23 Lesson 2

Sheet of lined paper (30)

Practice and Problem Solving Worksheets (30)

5. Vocabulary

The following mathematical vocabulary will be reviewed during this lesson: certain, likely, unlikely, and impossible. In the previous lesson, equally likely was presented to them, but not these words. Therefore, the teacher will explain and define these new words and show how each term is used within the context of the lesson. The teacher will also ask the students to listen, say, and write these words during the lesson. Furthermore, the teacher will also verbally recognize students who use these vocabulary terms during their responses and conversations.

6. Procedures

a. Preview and/or Review (Anticipatory Set)

|Instructional Strategies and Progress Monitoring |Student Activities |

|Preview: The teacher will explicitly state and write on the board the objective of |Students actively listen and chorally restate the |

|today’s lesson, which is to decide if an event is certain, likely, unlikely, or |objective. |

|impossible. Include equally certain. | |

|The teacher will explicitly state, explain, and model each vocabulary word |The students will listen, say, and then write the |

|presented. The teacher will write out each word on the board to provide vocal and |definitions on their piece of papers. |

|visual representation. This is important because by knowing the differences of each | |

|vocabulary word given, the students can utilize their knowledge into their work. | |

|To get the students to activate their prior knowledge, the teacher will draw 5 red |The students will listen and watch as boxes are drawn. |

|squares and 1 blue square on the white board. | |

| | |

|The teacher will ask the students, “Which color would you likely pick and why?” The |The students would talk amongst themselves and raise their |

|teacher will also ask the students to raise their hands to answer the question. |hands to answer the question while also giving their |

| |reason. |

| | |

|The teacher would also ask the students, “How would you describe the probability of |The students would listen and raise their hands to give a |

|the square you picked being blue?” |response to the question at hand. |

| | |

| | |

|Progress Monitoring (check for understanding): The teacher will draw different |The students will watch and listen as the teacher draws |

|colored boxes for each vocabulary word and will call upon students to see if they |boxes on the board. They will raise their hands if they |

|can determine if that set of boxes are certain, likely, unlikely or impossible. |believe they can answer one of the four questions drawn on |

| |the board. |

| | |

|The teacher will ask the class to repeat the vocabulary words in unison as the | |

|teacher points to teach word. “Certain, likely, unlikely, and impossible” |The students will repeat with the teacher the four |

| |vocabulary words. |

|The teacher will then restate the lesson objective and will mention that these words|Students will actively listen to the teacher’s explanation.|

|will be used in future lessons. | |

b. Explicit (Direct) Instruction (“I Do”)

|Instructional Strategies and Progress Monitoring |Student Activities: |

|The teacher will use the Houghton Mifflin Chapter 23 Lesson 2 Learn by Example |The students will actively listen to the teacher. |

|exercise (Pg. 498) to explain differences between certain, likely, unlikely, and | |

|impossible. | |

| | |

|Progress monitoring (check for understanding): The teacher will ask students in |The students will think about what the teacher has |

|their groups to share what was just demonstrated. The teacher will check students |explained and will write down any questions they have on |

|for understanding by listening to their use of academic vocabulary and answers any |their papers. |

|questions that they may still have. | |

| | |

|The teacher will explain that the students will now play the game “Grab Bag” in |With teacher direction, the students will first take their |

|order to develop further understanding of the differences between certain, likely, |bags and open them up. The students will take out the |

|unlikely, and impossible. |colored squares and set them on their desks. |

| | |

| |The students will then put back the squares in the bag. |

|The teacher will then tell the students that there are 5 red and 5 blue squares in | |

|the bag. The teacher will also explain that they are trying to figure out if their | |

|bags are certain, unlikely, likely, or impossible based on their colored squares | |

| | |

|The teacher will ask all students to see if they remember from their previous lesson|The students will talk amongst themselves can will raise |

|of the certainty of picking a blue square in the current bag of 5 red and 5 blue |their hands to come up with an answer. |

|squares. | |

| | |

|The teacher will then ask the students to all take out 5 red squares. The teacher |The students will take out 5 red squares and talk amongst |

|will ask, “What is the probability of picking a blue square class? And why? |their group to come up with an answer |

| | |

|Progress Monitoring (check for understanding): The teacher will move around and |A representative of the group will respond to teacher’s |

|closely look at student interactions. |question by raising their hand. |

| | |

|The teacher will then ask the students to replace the 5 red and take out 5 blue |The students will open their bags and stick the red squares|

|square. The teacher will ask, “What is the probability of picking a blue square |back in while removing 5 blue squares. They then talk |

|class? And why? |amongst themselves to come up with an answer. |

| | |

| |Students from each group may raise their hand to try and |

|Progress Monitoring (check for understanding): The teacher will move around and |answer the question |

|closely look at student interactions. | |

| |The students will open their bags and stick the blue |

|The teacher will then ask the students to replace the 5 blue squares and take out 2 |squares back in while removing 2 red squares. They will |

|red squares. The teacher will ask, “What is the probability of getting a blue square|talk amongst themselves to come up with an answer. |

|this time? And why? | |

| |A student from the group will patiently raise their hand to|

| |answer the question. |

|Progress Monitoring (check for understanding): The teacher will move around and | |

|closely look at student interactions. |The students will open their bags and stick the red squares|

| |back in the bag while removing 4 blue squares. They will |

|Then, the teacher will ask the students to replace removed squares and ask the |then try to answer the question by raising their hands. |

|students to remove 4 blue squares. The teacher will ask, “What is the probability of| |

|getting a blue square this time? |The students will raise hands to attempt to answer this |

| |question given by the teacher. |

| | |

|Progress Monitoring (check for understanding): The teacher will move around and | |

|closely look at student interactions. | |

|The teacher will write on the board all of the probabilities previously taught and |The students listen intently to the teacher’s lecture. |

|will go over them with the class. | |

c. Guided Practice (“We Do”)

|Instructional Strategies and Progress Monitoring |Student Activities |

|The teacher will draw a spinner on the board with two different colors. |The students will listen and watch the teacher. |

| | |

|The teacher will then ask the students to number their paper from one to five as the|The students will number their lined paper from one to five|

|teacher does the same on the board. |and wait patiently for further instructions. |

| | |

|The teacher will write questions on the board about different probability outcomes. |The students will write out the questions on their lined |

|The teacher will write out questions regarding probability and will ask the students|papers. |

|what the probabilities of the questions are. | |

| | |

|The teacher will first ask a group on the probability that the pointer will land on | |

|orange and why. |The students will answer the question after a few moments. |

| | |

|Progress Monitoring (check for understanding): The teacher will listen to the |The students will write a C on their papers when the |

|students answer and write a C by the number of the question if the student answered |correct answer is given and continue to listen and |

|correct. Also, if the student answered incorrectly, I will ask them if they are sure|participate in the guided lesson. |

|about their answer and give them another chance. | |

| | |

|The teacher will then ask another group on the probability that it will land on red | |

|and why. |The students in this group will take a few moments then |

| |answer the question accordingly. |

| | |

|Progress Monitoring (check for understanding): The teacher will again listen to the |The students will write a C on their papers when the answer|

|student’s response and write a C by the number if the student correctly answered the|is given correctly and listen to further instructions. |

|question. If the incorrect answer is given, the teacher will give the student | |

|another chance. | |

| |The students will converse and answer the question. |

|The teacher will ask the next group on the probability of the pointer landing on | |

|orange or blue and why. |The students will listen and continue to write notes and |

| |put a C on the correct answer on their paper. |

|Progress Monitoring (check for understanding): The teacher will listen and make sure| |

|the students understand the correct answer. The teacher will mark a C for the | |

|correct answer and if the incorrect answer is given, the teacher will give the | |

|student another chance. | |

| | |

| |The class will respond and give their reasoning as to why |

| |they think that their answer is the right one. |

|The teacher will ask the question to the entire class when the pointer will land on | |

|blue and why. |The student may ask questions about some of the answers and|

| |listen to further instructions. |

| | |

|Progress Monitoring (check for understanding): The teacher will respond to the class| |

|and will let then know if they answered the question correctly or incorrectly. The | |

|teacher will review the guided practice and go over the answers to make sure the | |

|students understood what was taught to them. | |

d. Independent Practice (“I Do”)

|Instructional Strategies and Progress Monitoring |Student Activities |

|The teacher will direct students to do the practice and problem solving worksheet, |The students will complete the rest of the problems |

|problems 8 through 11 on pg. 500. |independently. If they have difficultly, then they can ask |

| |for assistance from their group members. If they are having|

| |trouble as a group, the can have one of their group members|

| |raise their hands so that the teacher may assist them. |

| | |

| | |

| | |

|Progress Monitoring (check for understanding): While students are working | |

|independently, the teacher will oversee the class and check responses. When the | |

|student has the correct answer, the teacher will write a C for correct by the | |

|problem. If the response if incorrect, the teacher will explain to the student that | |

|it is incorrect and that the student should try again. If students are having | |

|difficulty with understanding the concept, the teacher will provide a small group | |

|instruction at front of the class by the white board. | |

e. Closure

|Instructional Strategies and Progress Monitoring |Student Activities |

|The teacher will review the lesson’s key vocabulary and mathematical concepts. The |The students will use their vocabulary in their lesson. The|

|teacher will then direct students to discuss what they learned in the lesson. The |students will also take a quiz to see if they learned |

|teacher will also give out a quiz to students for assessment that is on pg. 500. |anything. |

|For homework, the teacher will ask the students to find out the probability that a |The students will complete the assigned homework and turn |

|block of ice will melt at 68 degrees F (room temperature) by having them ask their |it in the next class session. |

|parents. The teacher will ask the students to write out their answers on a piece of | |

|paper and turn it in the next class session. | |

f. Back-up strategies:

For students who may have difficulty understanding the concepts of certain, likely, unlikely, and impossible, the teacher would go over with the students that certain and impossible are complete opposites. The teacher would explain that certain is absolute and that it will always happen and that impossible means that it will never happen. To explain to students about the differences between likely and unlikely, the teacher would explain that students can think of the concept of more than a half or less than a half. The teacher would show a diagram of items containing more than half, which are likely and that items less than half, which are unlikely. Other examples of strategies to help improve student learning would to be have students in groups. By doing this, I can have my students peer tutor each other to check and compare answers.

g. Rationale:

This lesson meets the third grade Academic Content Standard because it is taken directly from the district adopted and state approved textbook. Specifically, it addresses Statistics, Data Analysis, and Probability 1.1: Students are able to identify whether common events are certain, likely, unlikely, or impossible. This lesson also addresses Statistics, Data Analysis, and Probability 1.0, Mathematical Reasoning 1.0, Mathematical Reasoning 3.0, Mathematical Reasoning 3.2, and Mathematical Reasoning 3.3.

This lesson is developmentally appropriate for third grade students for several reasons. First, this is the students first time attempting to conduct simple experiments to determine outcomes and to make predictions based on those outcomes. This is challenging their critical thinking skills, and that is something that we want students to improve on. This lesson provides active engagement responses throughout---including the presentation of new vocabulary to the students, the ‘grab bag’ game activity, and the guided practice questions, along with the practice and problem worksheet. This lesson has been planned to incorporate cooperative and individual learning simultaneously. This lesson has been constructed to make sure that students master the lesson with the use of direct instruction, guided practice, independent practice, and closure. The progress monitoring that occurs throughout the lesson will allow the teacher to monitor and adjust instruction to meet the needs of students.

7. Assessment

Entry level assessment:

a. Three and two days prior to this lesson, students will have taken the Unit 8 Pre-assessments. These assessments will provide background knowledge about what students have learned and have retained from their second grade year. A review of assessment data from the students’ CST’s will also provide a picture of content mastery of the second grade standards. Also, informal assessments will give information as to the student’s strengths and weaknesses in completing the academic tasks necessary for successful completion of such tasks.

b. The teacher will use information gained from entry level assessments in lesson plans. The teacher will provide information on student weaknesses. For example, the teacher will re-teach concepts by other methods (back-up strategies), and future review lessons.

Progress Monitoring (informal, check for understanding):

By checking student responses and by moving about the room, the teacher can monitor the students’ progress throughout the entire lesson. During guided and independent practice, the teacher will carefully oversee individual student progress towards mastery. When the students answer correctly, the teacher will write a C for correct by the problem. If the student or students give an incorrect response, the teacher will ask the student to try a different method to see if he or she can come up with the correct solution. If not, the teacher can explain to the student the correct solution. If many students are having a difficult time with the same question, the teacher can use the white board or overhead to give direct instruction for those who need them.

Formal assessment:

The teacher will determine student mastery for this lesson by students completing the problems of this lesson with at least 80% accuracy. Additionally, at the end of the lesson, the students will be given homework to do with their parents.

8. Student and Parent Notification

Through close and careful progress monitoring, students will be aware of difficulties as soon as the teacher detects them. A parent newsletter will be sent home to parents at the beginning of each unit that explains what and how students will be learning math. The letter will include the vocabulary words that need to be learned and understood. Also, corrected work will also be sent home the next day with a grade. If students are having a hard time with assignments, a note will be added to notify the parent or parents about the situation. If further complications arise, the teacher will request for a parent teacher conference.

9. Periodic review, reinforcement, and practice

Students will complete the “Daily Routines” section at the beginning of the lesson. There is a Problem of the Day included on the Spiral Review, along with a Number Sense Review, a Number of the Day, and a Facts Practice. The students will complete a Leveled Practice and Writing depending on their needs. Extra practice and reinforcement will begin as soon as they complete the homework page. Furthermore, extra practice and reinforcement will occur in the latter lessons of this chapter, as the content has been spread out.

10. Adaptations for Special Needs Students (English learners and students with learning Problems)

|Adaptations |Rationale (how and why) |

|Students will be placed in groups in a way that they can all see the |By doing this, the teacher will ensure careful monitoring of students. |

|white board without having to turn around. Students with special needs |This is important, especially for the special needs students. |

|will be integrated with groups near the front of the class. | |

|Visual Cues, such as drawing charts, circles, squares, in color on the |By doing this, the teacher will make sure that the students can |

|white board. |understand what is being taught. This is helpful for visual learners, |

| |but adds to the learning process for students who have gained an |

| |understanding of the lesson. |

|The game “Grab Bag” |This game will help students learn the meaning of differences between |

| |certain, likely, unlikely, and impossible through student participation|

| |and activity. |

|Progress Monitoring throughout the lesson |By having the teacher closely monitor the guided and independent |

| |practices, the teacher will be able to see problems right away. If |

| |there is student difficulty, the teacher can use the guided practice |

| |procedures for the entire lesson. Also, careful monitoring helps the |

| |teacher to decide if the method of teaching needs to be changed to |

| |amplify the learning experience. |

|Individual Tutoring |The teacher can have an instructional aide or parent volunteer to |

| |assist the special needs students individually. After school assistance|

| |given by the teacher to special needs students is also a possibility. |

| |During class sessions, peer or cross-age tutoring may be an option. |

|Students repeat, summarize, and paraphrase |This will occur the entire lesson as the teacher monitors student |

| |responses. Whiteboards or thumbs up-thumbs down strategies are |

| |suggestions. |

|Choral responses by students |This will get the entire class involved so everyone is participating |

| |during the lesson. |

|Giving extra time for student response, and provide cues or hints |This will give students who have a hard time expressing their ideas |

| |time to express them. |

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